Question 31

Given that $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2 - 2bx + c = 0$$. The value of $$\alpha^4\beta^4 + \alpha^4\beta^3 + \alpha^3\beta^4$$ is equal to

From the equation, $$\alpha + \beta = 2b$$ and $$\alpha\beta = c$$. The expression equals $$(\alpha\beta)^4 + (\alpha\beta)^3(\alpha + \beta) = c^4 + c^3 \cdot 2b = c^3(c + 2b)$$.

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